Now I'm not saying that "eating disorders" are healthy (though definitions of "illness" and "wellness" change with the tides). I just don't see the communities of those who are in the midst of eating disorders as such a problem in need of banning. People are acting as if these are evil temptresses seducing others into sin. It reminds me of a church youth group handout on eating disorders that referenced the "body is the temple" passage and framed eating disorders as sinful behavior. But at least in our modern culture, many eating disorders seem to stem from social injustices of sexism, fatphobia, hyperindividualism, an overemphasis on self-determination, etc. Those are the problem. Not the people coping through extreme behaviors.
Some of the LJ petition signers use wording that makes me think they see "unhealthy" as "immoral." I can't equate people engaging in unhealthy behaviors together with immorality though. For me, this is mostly because of the scripture passage when Jesus said "it is not the healthy who need a doctor, but the sick." [Remembering that I have no formal theological training,] I don't hear him condoning the actions of the pharisees to whom he spoke and calling them moral and in no need of change. As best i can tell, that just wasn't his style. ;) So I don't hear him saying that healthy and good or moral are the same thing. When I read that, esp since he was being chastised for eating with tax collectors and prostitutes, I think he called "healthy" (but not necessarily good) those who are doing all right in the system as it currently stands, and "sick" (but not necessarily bad) those who manifest symptoms of injustice, experience harm, and even cope through behaviors they might not otherwise choose.
Anyway, I see the petitioning to ban such communities of people from gathering online as saying "we are currently healthy, you are unhealthy. And we all know healthy is good. So we are healthy and good. And you are sick and bad. So you need some of our healthy goodness to rub off on you, and we need to make sure your sick badness does not rub off on others, so tsk tsk no community for you until you change." A highly moralistic quarantine approach. It is completely different from how I see Jesus dealing with matters of "health."
(As a side note, I happen to believe dieting support communities and weight loss surgery support communities are also "encouraging unhealthy behavior" but again, the problem is not those communities. And they aren't being attacked because those manifestations of society's sins are welcomed, somewhat absolving even.)
ETA: These are all pretty scattered thoughts right now. I'd appreciate feedback and additional ideas.